As shown in FIGS. 1A and 1B, a conventional double offset joint 10 comprises an outer joint part 12, an inner joint part 14, a cage 16 and at least one ball 18. Typically, a plurality of balls 18 are provided. The outer joint part 10 has a cylindrical shape formed with a plurality of circumferentially spaced linear guide tracks 20 having a gothic arc or an elliptical form. The inner joint part 14 has circumferentially spaced linear guide tracks 22 formed on an outer spherical surface 24. The cage 16 retains the plurality of balls 18 in a plurality of pockets 26 circumferentially spaced about the cage 16. The cage 16 has an inner concave spherical surface at R2 and an outer convex spherical surface at R1. R1 and R2 are offset by e to the opposite sides of point O to points O1, O2 in the axial direction from the center of the ball pocket in which the outer convex spherical surface at R1 contacts a cylindrical bore 28 of the outer joint part 12. The inner concave spherical surface of the cage 16 at R2 contacts the outer convex spherical surface 24 of inner joint part 14. The inner joint part 14 also has an inner surface 30 for connection with a shaft (not shown).
In such a joint construction, if a certain torque is applied to the joint 10, a load acts on ball track 20, 22 or balls 18 in the direction normal to the ball track 20, 22. Another load derived partly from the load on the ball track 20, 22 acts on surfaces 32, 34 of the ball pockets 26 of the cage in axial direction Z, at an articulation angle. In this condition, the balls 18 contacts a track 20, 22 at the pressure angle A. A contact area CA is generated, taking the form of an ellipse defined by the longer length of elliptical contact a between the convex ball 18 and the concave track 22 and the shorter length of elliptical contact b made between the convex ball and the cylindrical formed track 20. However, a becomes equal to b on the surfaces 32, 33 of ball pocket 26, so the contact area takes a form of a circle, because a ball contacts a flat surface. The longer length of elliptical contact a on the ball track (hereafter contact ellipse length on ball track) and contact length on ball pocket (hereafter the contact length on the ball pocket) are design parameters to determine the cylindrical bore diameter of the outer joint part 12 in contact with outer spherical surface R1 of the cage 16 and the outer sphere diameter R2 of the inner joint part 14 in contact with the inner sphere diameter R2 of the cage 16. From this perspective, it is desirable that they (the cylindrical bore diameter of the outer joint part 12 and the outer sphere diameter of the inner joint part 14) be determined for the contact ellipse length a and not be cut off. If the contact ellipse length on the ball track or the ball pocket is cut off, contact stress on the ball track and the ball pocket increases by the amount of the cut off and affects durability of the joint 10.
In the event that a joint 10 rotates at an articulation angle B, best seen in FIG. 1C, a ball 18 reciprocates on the track 22 of the inner joint part 14 and the track 20 of the outer joint part 12. During the reciprocation of the ball 18, the distance between the pressure angle point and the bore diameter of outer joint part Lo does not vary along the ball track, due to its cylindrical shape, while that of the inner joint part Li varies along the ball track, due to its spherical shape defined by R2. More specifically, as the articulation angle increases, a ball 18 gets closer to the ends of the thickness of the inner joint part 14 on the ball track 22 and decreases the distance between the pressure angle point and the sphere diameter of the inner joint part Li, indicating that inner joint part 14 is inferior to the outer joint part 12 in terms of durability associated with the margin of contact in ellipse length a on the ball track. Furthermore, since the center of the outer sphere surface R2 is offset to a side O2 from the center O of the ball pocket at zero articulation angle, its diameter at the center of the ball pocket becomes RIO, as shown in FIG. 1A, so the inner joint part 12 is even inferior to the outer joint part 10 in terms of Li by difference of R2−RIO even at zero articulation angle.
At the same time, when a ball 18 reciprocates on the track, as shown in FIG. 1C, the ball 18 also moves in the radial direction and the circumferential direction on the surface of ball pocket 26. During the movement, one ball 18A moves closer to the edge of the outer spherical surface R1, while another ball 18B gets closer to the edge of the inner spherical surface R2 simultaneously in the radial direction, but it depends on the phase of the ball. In the worst case that either R1 or R2 is selected inadequately, a ball 18 could be derailed from the pocket 26. To prevent a ball 18 from being derailed from the pocket 26, the distance between the ball contact point and the inner spherical diameter (hereafter called cage inner spherical margin) S1 should be secured properly, as seen in FIG. 1A. Although a ball is not derailed from the ball pocket 26, contact stress on the surface of the ball pocket will increase by the contact length cut off, in case that S1 is smaller than the contact length a or b on the surface of the ball pocket 26. On the other hand, the rear opening diameter Rr should be greater than the outer spherical surface 22 diameter of the inner joint part 14 to get the inner joint part 14 assembled into the cage 16. It tends to make the distance between the rear opening diameter and the ball contact point on the ball pocket (hereafter called cage rear opening margin) S2 smaller than S1. Any attempt to increase the contact ellipse length a on the ball track 22 of the inner joint part 14 or on the ball track 20 of the outer joint part 12 without adjusting the other design parameters eventually causes the cage inner spherical margin S1, the cage rear opening margin S2 or the cage outer spherical margin SS1, SS2 to get smaller. Therefore, the contact ellipse length on ball track a and the contact length on the ball pocket a or b or the cage inner spherical margin S1, the cage outer spherical margin SS1, SS2, the cage rear opening margin S2 should be simultaneously considered for determining a bore diameter, outer spherical diameter, and inner spherical diameter, especially in terms of a compact design.
Recently, a lot of effort associated with compact design has been made to reduce the outside diameter of the outer joint part by increasing the number of balls, reducing the ball size, reducing the pitch circle diameter, and adjusting other design parameters, such as pressure angle and conformity ratio(=ball track radius/ball size). However, simple dimensional adjustments of design parameters in the conventional construction of double offset joint are not enough to achieve the compact design, due to the design constraints stated above, meaning that either the margin of the contact length on the ball pocket or the margin of contact of the ellipse length on the ball track is meant to be sacrificed to achieve the compact design, causing a reduction in either durability of the ball track or the durability of the cage ball pocket.